Tuesday, October 8, 2019

A Luni-Solar Connection to Weather and Climate III: Sub-Centennial Time Scales

Wilson, I.R.G. and Sidorenkov, N.S., 2019, A Luni-Solar Connection to Weather and Climate III: Sub-Centennial Time Scales, The General Science Journal, 7927
The following figure shows the raw HadCRUT4 monthly (Land + Sea) world mean temperature anomaly (WMTA) data from 1850 to 2017 (grey line – Climatic Research Unit, University of East Anglia, 2017).


Following the method used by Copeland and Watts (2009), a Hodrick Prescott filter (Hodrick and Prescott 1981 - using λ = 129,0000) is applied to the raw WMTA data to produce a smoothed temperature anomaly curve (Excel Plugin 2019). The resulting smoothed anomaly curve is superimposed upon the raw WMTA data in the figure below (red line).

The Hodrick Prescott filter is designed to separate a time-series data into a trend component and a cyclical component using a technique that is equivalent to a cubic spline smoother. It acts as a low-pass filter that smooths out short-term temperature fluctuations, leaving behind the unattenuated long-term oscillatory signals (Copland and Watts 2009). Given the specific value of λ used here, this effectively translates to a band-pass that eliminates all the oscillatory temperature signals that have periods ≤ 7.0 years (Copland and Watts 2009).

      Investigations of climate change generally involve the study of "forcings" upon the climate system. These are expressed in power terms that are measured in W m-2. This means that the best way to study temporal changes in these "forcings" is to look at time series of the first differences in the total energies that are associated with each forcing. Similarly, the mean temperature of the Earth's atmosphere is a measure of its total energy content. Thus, the best way to study the changes in the climate "forcings" that impact the mean temperature of the Earth's atmosphere is to look at time-series of the first difference in world-mean temperature, rather than time-series of the temperature itself [Goodman 2013].
     Following this train of logic, the first difference curve of the smoothed trend component of the WMTA time series is calculated in degrees Celsius per month. The resultant first difference curve (multiplied by an arbitrary factor of 150) is plotted in the figure below (blue curve). Superimposed upon this is the raw temperature anomaly data (light-grey curve) and the smoothed trend component (red curve), displayed in units of degrees Celsius.

The blue dashed curve in the figure below shows a superposition of a sine wave of amplitude 1.0 unit and period 9.1 tropical years with a sine wave of amplitude 2.0 units and period 10.1469 (= 9 FMC’s) tropical years. Note that the units used are degrees Celsius per month times 1000. The actual function used in this figure is:
where t is the date expressed in decimal Gregorian years [N.B. For the purposes of this study, this curve will be referred to as the lunar tidal forcing curve – i.e. LTF curve].

Overlaying this is a red curve which is simply a reproduction of the difference plot of the smoothed component of the WMTA from the earlier figure [N.B. For the purposes of this study, this curve will be referred to as the difference of the smoothed temperature anomaly curve – i.e. DSTA. It has units measured in degrees Celsius per month. In addition, the DSTA curve values have been scaled-up by a factor of 1000 to roughly match the variance of the LTF curve. This is done to aid the comparison between these two curves.

     A comparison of the DSTA and LTF curves shows that that the timing of the peaks in the LTF curve closely match those seen in the DSTA curve for two 45-year periods. 

     The first going from 1865 to 1910 and the second from 1955 to 2000. Note that these years are delineated by the black vertical lines in this figure. During these two epochs, the aligned peaks of the LTF and the DSTA curves are separated from adjacent peaks by roughly the 9.6 years, which is close to the mean of 9.1 and 10.1469 years. This is in stark contrast to the 45-year period separating these two epochs (i.e. from 1910 to 1955), and the period after the year 2000, where the close match between the timing of the peaks in LTF and DSTA curves breaks down, with the DSTA peaks becoming separated from their neighboring peaks by approximately 20 years.

     Hence, the variations in the rate of change of the smoothed HadCRUT4 temperature anomalies closely follow a “forcing” curve that is formed by the simple sum of two sinusoids, one with a 9.1-year period which matches that of the lunar tidal cycle, and the other with a period of 10.1469-year that matches that of half the Perigean New/Full moon cycle. This is precisely what you would expect if the natural periodicities associated with the Perigean New/Full moon tidal cycles were driving the observed changes in the world mean temperature on decadal time scales.


Copeland, B. and Watts, A., 2009, Evidence of a Luni-Solar Influence on the Decadal and Bi-decadal Oscillations in Globally Averaged Temperature Trends, retrieved at:

Lunar-Solar Influence on SST March 1st, 2013, Greg Goodman

Hodrick, R.  Prescott, E.,  1997, Postwar US business cycles: an empirical investigation.  Journal of Money, Credit, and Banking. 29(1): pp. 1-16. Reprint of University of Minneapolis discussion paper 451, 1981.

Thursday, October 3, 2019

Are the Strongest Lunar Perigean Spring Tides Commensurate with the Transit Cycle of Venus?

The following graph inspired my 2014 paper entitled:

Wilson, I.R.G. Are the Strongest Lunar Perigean Spring Tides Commensurate with the Transit Cycle of Venus?,  Pattern Recogn. Phys., 2, 75-93

Received: 25/Jul/2014 - Revised: 10/Sep/2014 - Accepted: 18/Sep/2014 - Published: 28/Nov/2014

It was accepted for publication in the second volume of the Journal Pattern Recognition in Physics (PRP) on the 18th of November 2014. The publishers of the PRP, Copernicus Publications, decided to close the journal in 2014, despite having accepted my paper for publication. It temporarily appeared on-line (i.e. was published) and then removed. In protest, I refused to pay the publication fee until they put my paper back up on-line. They never did.  I didn't realize that a publisher could accept a paper for publication, publish it and then remove it from publication, without giving any rational reason for their actions.

This graph shows the remarkable alignment between the dates for the transits of Venus over a 700-year period between 1600 and 2300 A.D. and the repetition pattern for the most extreme Perigean Spring tides that are closest to the nominal date of the Perihelion of the Earth's orbit. 


This study identifies the strongest perigean spring tides that reoccur at roughly the same time in the seasonal calendar and shows how their repetition pattern, with respect to the tropical year, is closely synchronized with the 243-year transit cycle of Venus. It finds that whenever the pentagonal pattern for the inferior conjunctions of Venus and the Earth drifts through one of the nodes of Venus’ orbit, the 31/62 year perigean spring tidal cycle simultaneously drifts through almost exactly the same days of the Gregorian year, over a period from 1 to 3000 A.D. Indeed, the drift of the 31/62 year tidal cycle with respect to the Gregorian calendar almost perfectly matches the expected long-term drift between the Gregorian calendar and the tropical year. If the mean drift of the 31/62 perigean spring tidal cycle is corrected for the expected long-term drift between the Gregorian calendar and the tropical year, then the long-term residual drift between: 

a) the 243-year drift-cycle of the pentagonal pattern for the inferior conjunctions of Venus and the Earth with respect to the nodes of Venus’s orbit and 

b) the 243-year drift-cycle of the strongest seasonal peak tides on the Earth (i.e. the 31/62 perigean spring tidal cycle) with respect to the tropical year,

is approximately equal to -7 ± 11 hours, over the 3000-year period. The large relative error of the final value for the residual drift means that this study cannot rule out the possibility that there is no long-term residual drift between the two cycles i.e. the two cycles are in perfect synchronization over the 3000 year period. However, the most likely result is a long-term residual drift of -7 hours, over the time frame considered.

Keywords: Solar System — Planetary Orbits — Lunar Tides 

Wednesday, September 18, 2019

The Easterly Trade Winds Over the Equatorial Pacific Ocean Have Disappeared Over the Last 5 Days or So!

UPDATED 22/09/2019 09:25 AEST
FURTHER UPDATED 28/09/2019 14:20 AEST

If you want to find out why go to the following post:


UPDATE 22/09/2019

On the 21 September 00:00 UTC, the equatorial trade winds in the Western Pacific are still dead, as far east as 165W!

Shown below are the Sea-Surface Temperature Anomalies (SSTA) for the 6th of September 00:00 UTC (on the right) and the 21st September 00:00UTC (on the left).

Note that warm surface water in the Western Pacific has moved eastward by ~ 3,300 km in 15 days.

The battle in between the warmer waters in the Western Pacific and the cooler waters in the Eastern Pacific Oceans.

Update 28/09/2019

Tuesday, September 17, 2019

Tropical Storms in the Equatorial Pacific Ocean are being triggered by the passage of Kelvin Waves

 N.B. If our claim is correct that Equatorial Kelvin Waves (EKWs) are being generated by the interaction between maxima in the lunar atmospheric/oceanic tides with minima in the diurnal sea-level pressure variations in the tropics (please read): 


then this post implies that the lunar tides must play a crucial role in initiating the Westerly Wind Bursts (WWBs) in the western equatorial Pacific ocean that are directly responsible for weakening the easterly equatorial trade winds that help trigger El Nino events.


If you visit Kyle MacRitchie's excellent blog site on Tropical waves at:


he states that convectively decoupled Equatorial Kelvin Waves (EKWs) can have outflows from their convection zones that cause Equatorial Rossby Wave (ERWs) trains to develop in their wake. 

He indicates that these ERWs aren't as strong as those created by MJOs since EKWs generally move from west-to-east along the Earth' equator at 3 to 4 times rate of Madden Julian Oscillations (MJOs).  

In addition, MacRitchie states that Kelvin waves provide favorable conditions for the development of Tropical Cyclones i.e. intense convection, low-level vorticity (in the form of trailing ERWs), vertical shear, and mid-level moisture.


I light of this, we present a report on the passage of a convectively-decoupled Kelvin Wave across the Equatorial Pacific Ocean, over the last several days, that has set off a series of weak tropical storms and possibly one Hurricane.

The following plot shows the location of MJOs in the equatorial regions of the Indo-Pacific (as represented by the MJO phase - vertical axis) for times between May 15th and September 15th, 2019 (horizontal axis).

This plot showed that the most recent MJO event:

a) started off the east coast of equatorial Africa (MJO Phase 1) around the 17th of August, 

b) reached the region on the Equator between the Philippines and New Guinea (MJO phase 5), around about the 4th -- 5th of September, where it started producing Westerly Wind Bursts (WWBs) to the north of Papua New Guinea.

c) generated a convectively decoupled Kelvin wave, most likely around September 8th, that began moving out across the equatorial Pacific Ocean at a speed of roughly 1350 km/day, reaching the coast of South America roughly 9 -- 10 days later.  

The following weather map shows that the passage of the convectively decoupled Kelvin wave (between September 8th to 17th) generated at least 5 weak topical tropical storms and possibly one hurricane, straddling the Earth's equator at roughly 15 degrees north latitude.

Ref: (https://earth.nullschool.net/)

The following plots show that:

1) the MJO event produces WWBs in the western equatorial Pacific ocean between the 8th and 11th of September.

2) the convectively de-coupled EKW that emerges from the MJO event (sometime after September 8th) starts to move across the equatorial Pacific ocean leaving a series of weak tropical storms in its wake (starting on September 13th), straddling the Earth's equator at roughly 15 degrees North latitude.

3) the cumulative westerly wind flows that are produced on the southern sides of this string of tropical storms effectively eliminates the easterly equatorial trade winds as far east as the mid-Pacific ocean, at 160 degrees West longitude (N.B. the red vertical line on the Equator marks the most easterly longitude of the stalled trade winds for that date).

 All it would take is a series of vigorous EKWs like this one to trigger a major El Nino event, showing that the lunar atmospheric/oceanic tides must play a role in initiating these significant climate events.  

8th Sept

9th Sept

10th Sept

11th Sept

12th Sept

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14th Sept

15th Sept

16th Sept

17th Sept

Friday, September 6, 2019

A lunar tidal mechanism for generating Equatorial Kelvin waves

To find out more details about the lunar tidal mechanism that could generate Equatorial Kelvin waves, please read the following post.

 Please click on the diagram below to activate the GIF animation

If you were to observe the Moon from a fixed point on the Equator at the same time each day, you would notice that the sub-lunar point on the Earth's surface appears to move at a speed of 15 — 20 m/sec from west-to-east. This results from the fact that the west-to-east speed of the Moon along the Ecliptic (as seen from the Earth’s center) varies between 15.2 — 19.8 m/sec. 

Interestingly, the west-to-east group (and phase) velocity for the convectively-decoupled Equatorial Kelvin wave (EKW) is 15 — 20 m/sec, as well. This remarkable "coincidence" raises the question:

Could it be that easterly moving convectively-decoupled EKW are produced by the interaction between the day-to-day movement of the lunar-induced atmospheric/oceanic tides with a meteorological phenomenon that routinely occurs at roughly the same time each (24 hr) solar day?

One meteorological phenomenon that fits this bill is the atmospheric surface pressure variations measured at any given fixed location in the tropics. At many points near the equator, the atmospheric surface pressure spends much of its time sinusoidally oscillating about its long-term mean with an amplitude of 1 to 2 hPa (or millibars). Generally, this regular daily oscillation is only disrupted by the passage of a tropical low-pressure cell (e.g. tropical lows, tropical storms, and Hurricanes, Typhoons, and Cyclones).

For example, figure 1 shows the diurnal surface pressure variations in the Carribean as measured by Haurwitz (1947). What this figure indicates is that, like many points near the Earth's equator, the atmospheric surface pressure reaches a minimum near 4:00 -- 4:30 a.m. and 4:00 -- 4:30 p.m.

Figure 1

Source; Figure 1 of Haurwitz B., 1947, Harmonic Analysis of the Diurnal Variations of Pressure and Temperature Aloft in the Eastern Caribbean, Bulletin of the American Meteorological Society, Vol. 28, pp. 319-323.  
This leads us to propose the hypothesis that:


EKWs are generated when the peak in the lunar-induced tides passes through the local meridian at roughly 4:00 a.m. and 4:00 p.m. local time, when the diurnal surface pressure is a minimum. This type of lunar tidal event takes place once every half synodic month = 14.77 days.

Some important points to note:

* The lunar-induced tidal peak in the atmosphere and oceans passes through the local meridian (during its daily passage from west-to-east) both when the Moon is passing through the meridian, and when the Moon is passing through the anti-meridian. This is due to the semi-diurnal nature of the tides.

** If you select times when the Moon passes through the local meridian at a fixed time (e.g. 4:00 p.m. or 4:00 a.m.), you are in fact selecting times when the Moon is at a specific phase (or a fixed point in the Synodic month). Hence, when the Moon is passing through the meridian at 4:00 p.m., the Moon has a Waxing Crescent phase (~33.3 %), and when the Moon is passing through the local anti-meridian at 4:00 p.m. it has a Waning Gibbous phase (~33.3 %).

The following diagram shows a view of the Earth (fawn-colored circle) as seen from above the North Pole, in a frame-of-reference that is fixed with respect to the Sun. In this frame-of-reference, the Earth rotates and the Moon revolves in a clockwise direction. Included in this diagram is a light blue elliptical annulus that represents the sea-level atmospheric pressure at the Earth's equator. This ellipse highlights the fact that the sea-level atmospheric pressure is typically a minimum at 4 a.m. and 4 p.m., and a maximum at 10 a.m. and 10 p.m. In addition, there is a dark blue elliptical annulus that represents the lunar-induced tides in the Earth's atmosphere and oceans. 

If you click on the gif animation you will see the lunar-induced tidal peak at 4.00 a.m. (4.00 p.m.) move to 4.00 p.m. (4.00 a.m.) over a 14.77 day period, where it induces an atmospheric Kelvin wave that travels along the Earth's equator from west-to-east at a speed of 15 -- 20 m/sec. Then you will see the whole process repeat itself when the lunar-induced tidal peak at 4.00 p.m. (4.00 a.m.) moves to 4.00 a.m. (4.00 p.m.) over the remaining 14.77 days of the lunar Synodic cycle.       

Please click on the diagram below to activate the GIF animation